Onlinetuition.com SPM Additional Mathematics
Question 6: Find the number of the multiples of 8 between 100 and 300. Solution: Question 7: Find the sum of all the multiples of 7 between 100 and 500. Solution: Question 8: If log 10 p, log 10 pq and log 10 p q 2 are the first three terms of a progression, show that … Read more
Question 1: The third and eighth terms of an arithmetic progression are –5 and 15 respectively. Find (a) The first term and the common difference (b) The sum of the first 10 terms. Solution: (a) T 3 =−5 → Use T n =a+( n−1 )d a+2d=−5→( 1 ) T 8 =15 a+7d=15→( 2 ) ( 2 )−( … Read more
Question 11 Given that 2 log2 (x – y) = 3 + log2x + log2 y. Prove that x2 + y2– 10xy = 0. Solution: 2 log2 (x – y) = 3 + log2x + log2 y log2 (x– y)2 = log2 8 + log2 x + log2y log2 (x– y)2 = log2 8xy (x … Read more
Question 8 Solve the equation, log 9 ( x − 2 ) = log 3 2 Solution: log 9 ( x − 2 ) = log 3 2 log a b = log c b log c a ⇒ log 3 ( x − 2 ) log 3 9 = log 3 2 log 3 … Read more
METHOD:For two logarithms of the same base, if log a m = log a n , then m = n . Convert to index form, if log a m = n , then m = an. Example 1Solve the following equation:(a) log 3 2 + log 3 ( x + 5 ) = log 3 … Read more
METHOD: Comparison of indices or base If the base are the same , when a x = a y , then x = y If the index are the same , when a x = b x , then a = b Using common logarithm (If base and index are NOT the same) a x … Read more
Change of Base of Logarithms log a b= log c b log c a and log a b= 1 log b a Example: Find the value of the following: a. log 25 100 b. log 3 0.45 Answer: (a) log 25 100= log 10 100 log 10 25 = log 10 10 … Read more
4.3 Logarithms N = a x ⇔ log a N = x log a N = x is called the logarithmic form and N = a x is the index or exponential form. Note: The logarithm of a negative number is not defined. log in … Read more
(A) Steps in solving simultaneous equations involving one linear equation and one non-linear equation: For the linear equation, arrange so that one of the unknown becomes the subject of the equation. Substitute the linear equation into the non-linear equation. Simplify and expressed the equation in the general form of quadratic equation a x 2 + … Read more
Question 31 (SPM 2019):Diagram 1 shows the graph of a quadratic function$$ f(x)=\frac{p}{x^n}+q x+r $$such that p, q, r, n and u are constants.(a) State the value of n.(b) If f(x) = 0 and the product of roots is r, state the value of (i) q,(ii) p.[3 marks] Answer:(a)$$ \begin{aligned} & x^{-n}=x^2 \\ & -n=2 \\ … Read more